{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 03 - 统计回顾：最危险的公式\n",
    "\n",
    "在 2007 年的著名文章中，霍华德·韦纳 (Howard Wainer) 针对非常危险的公式做了如下说明[1]：\n",
    "\n",
    "“有些公式如果你知道它们的话会很危险，而另一些公式如果你不知道它们则会很危险。第一类之所以可能会带来危险，是因为这些公式揭示了通往背后隐藏着的可怕危险。这其中最著名的是爱因斯坦相对论的经典公式：\\\\\\ (E = MC^2\\\\)，因为它揭开了隐藏在普通物质中的巨大能量。... 另一方面，我对那些当我们不知道的时候会带来危险，而当我们明白了道理后反而没有问题的公式更感兴趣。当我们熟悉这些公式的时候，它们能让我们能够清楚地理解事物，但一旦不了解就会让我们处在无知的危险中。”\n",
    "\n",
    "他所说的就是 Moivre 公式：\n",
    "\n",
    "$\n",
    "SE = \\dfrac{\\sigma}{\\sqrt{n}}\n",
    "$\n",
    "\n",
    "其中 \\\\(SE\\\\) 是平均值的标准误差，\\\\(\\sigma\\\\) 是标准偏差，\\\\(n\\\\) 是样本大小。听起来像一个勇敢而真实的人应该掌握的数学，所以让我们开始认真学习它。\n",
    "\n",
    "要了解为什么不知道这个等式是非常危险的，让我们来看看一些教育数据。我已经收集了来自不同学校的 ENEM 分数（巴西标准化高中分数，类似于 SAT）的数据，为期 3 年。我还对数据进行了一些清理，只保留与我们相关的信息。原始数据可在[Inep网站](http://portal.inep.gov.br/web/guest/microdados#)下载。\n",
    "\n",
    "如果我们看看表现最好的学校，就会注意到一些事情：这些学校的学生人数相当少。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import warnings\n",
    "warnings.filterwarnings('ignore')\n",
    "\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "from scipy import stats\n",
    "import seaborn as sns\n",
    "from matplotlib import pyplot as plt\n",
    "from matplotlib import style\n",
    "style.use(\"fivethirtyeight\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>year</th>\n",
       "      <th>school_id</th>\n",
       "      <th>number_of_students</th>\n",
       "      <th>avg_score</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>16670</th>\n",
       "      <td>2007</td>\n",
       "      <td>33062633</td>\n",
       "      <td>68</td>\n",
       "      <td>82.97</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16796</th>\n",
       "      <td>2007</td>\n",
       "      <td>33065403</td>\n",
       "      <td>172</td>\n",
       "      <td>82.04</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16668</th>\n",
       "      <td>2005</td>\n",
       "      <td>33062633</td>\n",
       "      <td>59</td>\n",
       "      <td>81.89</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16794</th>\n",
       "      <td>2005</td>\n",
       "      <td>33065403</td>\n",
       "      <td>177</td>\n",
       "      <td>81.66</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10043</th>\n",
       "      <td>2007</td>\n",
       "      <td>29342880</td>\n",
       "      <td>43</td>\n",
       "      <td>80.32</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18121</th>\n",
       "      <td>2007</td>\n",
       "      <td>33152314</td>\n",
       "      <td>14</td>\n",
       "      <td>79.82</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16781</th>\n",
       "      <td>2007</td>\n",
       "      <td>33065250</td>\n",
       "      <td>80</td>\n",
       "      <td>79.67</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3026</th>\n",
       "      <td>2007</td>\n",
       "      <td>22025740</td>\n",
       "      <td>144</td>\n",
       "      <td>79.52</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14636</th>\n",
       "      <td>2007</td>\n",
       "      <td>31311723</td>\n",
       "      <td>222</td>\n",
       "      <td>79.41</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17318</th>\n",
       "      <td>2007</td>\n",
       "      <td>33087679</td>\n",
       "      <td>210</td>\n",
       "      <td>79.38</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       year  school_id  number_of_students  avg_score\n",
       "16670  2007   33062633                  68      82.97\n",
       "16796  2007   33065403                 172      82.04\n",
       "16668  2005   33062633                  59      81.89\n",
       "16794  2005   33065403                 177      81.66\n",
       "10043  2007   29342880                  43      80.32\n",
       "18121  2007   33152314                  14      79.82\n",
       "16781  2007   33065250                  80      79.67\n",
       "3026   2007   22025740                 144      79.52\n",
       "14636  2007   31311723                 222      79.41\n",
       "17318  2007   33087679                 210      79.38"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.read_csv(\"./data/enem_scores.csv\")\n",
    "df.sort_values(by=\"avg_score\", ascending=False).head(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "换个角度看，我们只能把1%的顶尖学校分开来研究。 他们像什么？ 也许我们可以从最好的那里学到一些东西并在其他地方复制它。 果然，如果我们看看排名前 1% 的学校，我们会发现他们的学生平均更少。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_data = (df\n",
    "             .assign(top_school = df[\"avg_score\"] >= np.quantile(df[\"avg_score\"], .99))\n",
    "             [[\"top_school\", \"number_of_students\"]]\n",
    "             .query(f\"number_of_students<{np.quantile(df['number_of_students'], .98)}\")) # remove outliers\n",
    "\n",
    "plt.figure(figsize=(6,6))\n",
    "sns.boxplot(x=\"top_school\", y=\"number_of_students\", data=plot_data)\n",
    "plt.title(\"Number of Students of 1% Top Schools (Right)\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "随之而来的一个自然结论是，小班教学会带来更高的学业成绩。 这具有直观的意义，因为我们相信每位教师的学生越少，教师就越可以专注于每个学生。 但这与 Moivre 方程有什么关系呢？ 为什么它是危险的？\n",
    "\n",
    "好吧，一旦人们开始根据这些信息做出重要且代价高昂的决定，就会变得危险。 在他的文章中，霍华德继续说道：\n",
    "\n",
    "“在 1990 年代，支持缩小学校规模变得流行起来。许多慈善组织和政府机构根据规模较小的学校的学生在考试成绩高的群体中人数过多的事实，资助了大学校的划分。”\n",
    "\n",
    "人们忘记做的是还要看看排名垫底的 1% 的学校。 如果我们这样做，瞧！ 他们的学生也很少！"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "q_99 = np.quantile(df[\"avg_score\"], .99)\n",
    "q_01 = np.quantile(df[\"avg_score\"], .01)\n",
    "\n",
    "plot_data = (df\n",
    "             .sample(10000)\n",
    "             .assign(Group = lambda d: np.select([d[\"avg_score\"] > q_99, d[\"avg_score\"] < q_01],\n",
    "                                                 [\"Top\", \"Bottom\"], \"Middle\")))\n",
    "plt.figure(figsize=(10,5))\n",
    "sns.scatterplot(y=\"avg_score\", x=\"number_of_students\", hue=\"Group\", data=plot_data)\n",
    "plt.title(\"ENEM Score by Number of Students in the School\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "我们在上面看到的正是根据 Moivre 方程所预期的。随着学生人数的增加，平均分变得越来越精确。样本很少的学校可能会因为偶然而获得非常高和非常低的分数。大型学校不太可能发生这种情况。 Moivre 的方程谈到了一个现实中关于信息和数据形式记录的基本事实：它总是不精确的。那么问题就变为，到底有多么不精确。\n",
    "\n",
    "统计学是处理这些不精确性的科学，因此它们不会让我们措手不及。正如塔勒布在他的书《被随机性愚弄》中所说：\n",
    "\n",
    "> 概率不仅仅是计算骰子或更复杂的变体的几率；它是接受我们的知识缺乏确定性和发展处理我们的无知的方法。\n",
    "\n",
    "量化我们的不确定性的一种方法是**我们的估计值的方差**。方差告诉我们观察值偏离了它们的中心值和最可能值的程度。正如 Moivre 方程所示，这种不确定性随着我们观察到的数据量的增加而缩小。这是有道理的，对吧？如果我们看到很多学生在学校表现出色，我们就会更有信心这确实是一所好学校。但是，如果我们看到一个只有 10 名学生并且其中 8 名学生表现良好的学校，我们需要多加怀疑。可能是因为偶然，这所学校有一些高于平均水平的学生。\n",
    "\n",
    "我们上面看到的美丽的三角形图正是讲述了这个故事。它向我们展示了当样本量很小时，我们对学校表现的估计如何存在巨大差异。它还表明方差随着样本量的增加而缩小。这对于学校的平均分数是正确的，但对于我们拥有的任何汇总统计数据也是如此，包括我们经常想要估计的 ATE。\n",
    "\n",
    "## 我们估计值的标准误差\n",
    "\n",
    "由于这只是对统计数据的回顾，我现在冒昧地讲得更快一些。如果您不熟悉分布、方差和标准误差，请继续阅读，但请记住，您可能需要一些额外的资源。我建议你用谷歌搜索任何麻省理工学院关于统计介绍的课程。他们通常都很好。\n",
    "\n",
    "在上一节中，我们将平均处理效果 \\\\(E[Y_1-Y_0]\\\\) 估计为处理和未处理之间均值的差异 \\\\(E[Y|T=1]-E[Y |T=0]\\\\)。作为我们的示例，我们为在线课程找到了 \\\\(ATE\\\\)。我们还看到这是一个负面影响，即在线课程使学生的表现比面对面课程的学生差 5 分左右。现在，我们可以看看这种影响在统计上是否显着。\n",
    "\n",
    "为此，我们需要估计 \\\\(SE\\\\)。我们已经有了 \\\\(n\\\\)，我们的样本大小。要获得标准偏差的估计值，我们可以执行以下操作\n",
    "\n",
    "$\n",
    "\\hat{\\sigma}^2=\\frac{1}{N-1}\\sum_{i=0}^N (x-\\bar{x})^2\n",
    "$\n",
    "\n",
    "其中 \\\\(\\bar{x}\\\\) 是 \\\\(x\\\\) 的平均值。对我们来说幸运的是，大多数编程软件已经实现了这一点。在 Pandas 中，我们可以使用方法 [std](https://pandas.pydata.org/pandas-docs/stable/reference/api/pandas.DataFrame.std.html)。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "SE for Online: 1.5371593973041635\n",
      "SE for Face to Face: 0.8723511456319106\n"
     ]
    }
   ],
   "source": [
    "data = pd.read_csv(\"./data/online_classroom.csv\")\n",
    "online = data.query(\"format_ol==1\")[\"falsexam\"]\n",
    "face_to_face = data.query(\"format_ol==0 & format_blended==0\")[\"falsexam\"]\n",
    "\n",
    "def se(y: pd.Series):\n",
    "    return y.std() / np.sqrt(len(y))\n",
    "\n",
    "print(\"SE for Online:\", se(online))\n",
    "print(\"SE for Face to Face:\", se(face_to_face))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 置信区间\n",
    "\n",
    "我们估计的标准误差是置信度的衡量标准。为了准确理解它的含义，我们需要进入充满争论的统计领域。对于统计学的一种观点，即频率学派的观点，我们会说我们拥有的数据只不过是真实数据生成过程的一种表现。这个过程是抽象的和理想的。它由不变但我们不知道的真实参数控制。在学生测试的背景下，如果我们可以运行多个实验并收集多个数据集，所有这些都将类似于真正的底层数据生成过程，但不会完全如此。这很像柏拉图在形式上的写作：\n",
    "\n",
    "> 每一种$[$基本形式$]$都表现在各种各样的组合中，有行为，有物质，还有彼此，每一种似乎都有很多\n",
    "\n",
    "为了更好地理解这一点，让我们假设我们有一个学生考试成绩的真实抽象分布。这是一个正态分布，真实平均值为 74，真实标准差为 2。从这个分布中，我们可以运行 10000 次实验。在每一个上，我们收集 500 个样本。有些实验数据的平均值会低于真实数据，有些会更高。如果我们将它们绘制在直方图中，我们可以看到实验的均值分布在真实均值附近。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "true_std = 2\n",
    "true_mean = 74\n",
    "\n",
    "n = 500\n",
    "def run_experiment(): \n",
    "    return np.random.normal(true_mean,true_std, 500)\n",
    "\n",
    "np.random.seed(42)\n",
    "\n",
    "plt.figure(figsize=(8,5))\n",
    "freq, bins, img = plt.hist([run_experiment().mean() for _ in range(10000)], bins=40, label=\"Experiment Means\")\n",
    "plt.vlines(true_mean, ymin=0, ymax=freq.max(), linestyles=\"dashed\", label=\"True Mean\", color=\"orange\")\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "请注意，我们在这里讨论的是均值的均值。因此，假如我们有机会进行一个实验，其中均值可能会略低于或高于真实均值。这就是说，我们永远无法确定实验的均值是否与真正的柏拉图式和理想均值相匹配。但是，**使用标准误差，我们可以创建一个区间，该区间将包含 95% 的时间的真实平均值**。\n",
    "\n",
    "在现实生活中，我们无法用多个数据集模拟同一个实验。我们经常只有一个。但是我们可以利用上面的直觉来构建我们所说的**置信区间**。置信区间附带一个概率。最常见的是95%。这个概率告诉我们从不同的研究中建立的假设置信区间有多少包含真实的平均值。例如，从许多类似研究计算的 95% 置信区间将包含 95% 的时间的真实平均值。\n",
    "\n",
    "为了计算置信区间，我们使用所谓的**中心极限定理**。该定理指出**实验均值是正态分布的**。从统计理论中，我们知道 95% 的正态分布的质量介于均值上下 2 个标准差之间。从技术上讲，1.96，但 2 已经足够接近了。\n",
    "\n",
    "![normal_density](./data/img/stats-review/normal_dist.jpeg)\n",
    "\n",
    "均值的标准误差用作我们对实验均值分布的估计。因此，如果我们将其乘以 2 并从我们的一个实验的平均值中加上和减去它，我们将为真实平均值构建一个 95% 的置信区间。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(73.82718114045632, 74.17341543460314)\n"
     ]
    }
   ],
   "source": [
    "np.random.seed(321)\n",
    "exp_data = run_experiment()\n",
    "exp_se = exp_data.std() / np.sqrt(len(exp_data))\n",
    "exp_mu = exp_data.mean()\n",
    "ci = (exp_mu - 2 * exp_se, exp_mu + 2 * exp_se)\n",
    "print(ci)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(exp_mu - 4*exp_se, exp_mu + 4*exp_se, 100)\n",
    "y = stats.norm.pdf(x, exp_mu, exp_se)\n",
    "plt.plot(x, y)\n",
    "plt.vlines(ci[1], ymin=0, ymax=1)\n",
    "plt.vlines(ci[0], ymin=0, ymax=1, label=\"95% CI\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "当然，我们不需要将自己限制在 95% 的置信区间内。 我们可以通过找到我们需要乘以标准差来生成 99% 的区间，因此该区间包含 99% 的正态分布质量。\n",
    "\n",
    "python 中的函数 ppf 为我们提供了 CDF 的倒数。 因此，ppf(0.5) 将返回 0.0，表示标准正态分布质量的 50% 低于 0.0。 同理，如果我们插入 99.5%，我们将得到 z 值，这样 99.5% 的分布质量会低于这个值。 换句话说，质量的 0.05% 落在此值以上。 我们不是像找到 95% CI 那样将标准误差乘以 2，而是将其乘以 z，这将得到 99% CI。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.5758293035489004\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(73.7773381773405, 74.22325839771896)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from scipy import stats\n",
    "z = stats.norm.ppf(.995)\n",
    "print(z)\n",
    "ci = (exp_mu - z * exp_se, exp_mu + z * exp_se)\n",
    "ci"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(exp_mu - 4*exp_se, exp_mu + 4*exp_se, 100)\n",
    "y = stats.norm.pdf(x, exp_mu, exp_se)\n",
    "plt.plot(x, y)\n",
    "plt.vlines(ci[1], ymin=0, ymax=1)\n",
    "plt.vlines(ci[0], ymin=0, ymax=1, label=\"99% CI\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "回到我们的课堂实验，我们可以为在线和面对面学生组的平均考试分数构建置信区间"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "95% CI for Online: (70.56094429049804, 76.7095818797147)\n",
      "95% for Face to Face: (76.80278229206948, 80.29218687459712)\n"
     ]
    }
   ],
   "source": [
    "def ci(y: pd.Series):\n",
    "    return (y.mean() - 2 * se(y), y.mean() + 2 * se(y))\n",
    "\n",
    "print(\"95% CI for Online:\", ci(online))\n",
    "print(\"95% for Face to Face:\", ci(face_to_face))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "我们可以看到的是，组的 95% CI 不重叠。面对面课程的 CI 的下端高于在线课程的 CI 的上端。这证明我们的结果并非偶然，面对面课堂学生的真实平均值高于在线课程学生的真实平均值。换句话说，从面对面切换到在线课程时，学习成绩会显着下降。\n",
    "\n",
    "回顾一下，置信区间是一种为我们的估计设置不确定性的方法。样本量越小，标准误越大，置信区间越宽。最后，您应该始终对没有附加任何不确定性指标的测量保持怀疑。由于它们非常容易计算，因此缺乏置信区间表示一些不良意图或只是缺乏知识，这同样令人担忧。\n",
    "\n",
    "![img](data/img/stats-review/ci_xkcd.png)\n",
    "\n",
    "在此最后提醒一句。置信区间比乍一看更难解释。例如，我**不应该**说这个特定的 95% 置信区间包含 95% 机会的真实总体均值。这是因为在频率统计（使用置信区间的统计）中，总体均值被视为真正的总体常数。所以它要么在我们特定的置信区间内，要么不在。换句话说，我们的特定置信区间包含或不包含真实均值。如果是这样，包含它的机会将是 100%，而不是 95%。如果不是，则可能性为 0%。相反，在置信区间中，95% 是指在许多研究中计算出的此类置信区间包含真实平均值的频率。 95% 是我们对用于计算 95% CI 的算法的置信度，而不是特定区间本身。\n",
    "\n",
    "现在，话虽如此，作为一名经济学家（统计学家，现在请移开视线），我认为这种纯粹主义不是很有用。在实践中，您会看到人们说特定的置信区间在 95% 的情况下都包含真实均值。尽管这是错误的，但这并不是很有害，因为它仍然在我们的估计中存在一定程度的不确定性。此外，如果我们切换到贝叶斯统计并使用概率区间而不是置信区间，我们可以说该区间在 95% 的时间内包含分布均值。此外，从我在实践中看到的情况来看，在样本量不错的情况下，贝叶斯概率区间与置信区间比贝叶斯和频率论者都愿意承认的更相似。所以，如果我的话对任何事情都很重要，请随意说出你想要的关于你的置信区间的任何内容。我不在乎您是否说它们在 95% 的情况下都包含真实平均值。只是，请永远不要忘记将它们放在您的估计周围，否则您会看起来很傻。\n",
    "\n",
    "\n",
    "＃＃ 假设检验\n",
    "\n",
    "包含不确定性的另一种方法是陈述假设检验：均值差异在统计上与零（或任何其他值）不同吗？为此，我们将回忆起 2 个独立正态分布的和或差也是正态分布。结果均值将是两个分布之间的总和或差，而方差始终是方差之和：\n",
    "\n",
    "$\n",
    "N(\\mu_1, \\sigma_1^2) - N(\\mu_2, \\sigma_2^2) = N(\\mu_1 - \\mu_2, \\sigma_1^2 + \\sigma_2^2)\n",
    "$\n",
    "\n",
    "$\n",
    "N(\\mu_1, \\sigma_1^2) + N(\\mu_2, \\sigma_2^2) = N(\\mu_1 + \\mu_2, \\sigma_1^2 + \\sigma_2^2)\n",
    "$\n",
    "\n",
    "如果你不记得，没关系。我们可以随时使用代码和模拟数据来检查："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.random.seed(123)\n",
    "n1 = np.random.normal(4, 3, 30000)\n",
    "n2 = np.random.normal(1, 4, 30000)\n",
    "n_diff = n2 - n1\n",
    "sns.distplot(n1, hist=False, label=\"N(4,3)\")\n",
    "sns.distplot(n2, hist=False, label=\"N(1,4)\")\n",
    "sns.distplot(n_diff, hist=False, label=f\"NN(1,4) - (4,3) = N(-1, 5)\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "如果我们取两组均值的分布并从另一个中减去一个，我们将得到第三个分布。 该最终分布的均值将是均值的差值，该分布的标准差将是标准差总和的平方根。\n",
    "\n",
    "$\n",
    "\\mu_{diff} = \\mu_1 - \\mu_2\n",
    "$\n",
    "\n",
    "$\n",
    "SE_{diff} = \\sqrt{SE_1 + SE_2} = \\sqrt{\\sigma_1^2/n_1 + \\sigma_2^2/n_2}\n",
    "$\n",
    "\n",
    "让我们回到我们的课堂例子。 我们将构建这种差异分布。 当然，一旦我们有了它，构建 95% CI 就非常容易了。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(-8.376410208363357, -1.4480327880904964)\n"
     ]
    }
   ],
   "source": [
    "diff_mu = online.mean() - face_to_face.mean()\n",
    "diff_se = np.sqrt(face_to_face.var()/len(face_to_face) + online.var()/len(online))\n",
    "ci = (diff_mu - 1.96*diff_se, diff_mu + 1.96*diff_se)\n",
    "print(ci)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(diff_mu - 4*diff_se, diff_mu + 4*diff_se, 100)\n",
    "y = stats.norm.pdf(x, diff_mu, diff_se)\n",
    "plt.plot(x, y)\n",
    "plt.vlines(ci[1], ymin=0, ymax=.05)\n",
    "plt.vlines(ci[0], ymin=0, ymax=.05, label=\"95% CI\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "有了这个，我们可以说我们有 95% 的信心在线和面对面组之间的真正差异介于 -8.37 和 -1.44 之间。我们还可以通过将均值差异除以差异的 \\\\\\(SE\\\\\\\\) 来构建 **z 统计量**。\n",
    "\n",
    "$\n",
    "z = \\dfrac{\\mu_{diff} - H_{0}}{SE_{diff}} = \\dfrac{(\\mu_1 - \\mu_2) - H_{0}}{\\sqrt{\\sigma_1^2/n_1 + \\sigma_2^2/n_2}}\n",
    "$\n",
    "\n",
    "其中 \\\\(H_0\\\\) 是我们要测试差异的值。\n",
    "\n",
    "z 统计量衡量观察到的差异的极端程度。为了检验均值差异在统计上不同于零的假设，我们将使用矛盾。我们将假设相反的情况是正确的，即我们将假设差异为零。这称为零假设，或 \\\\(H_0\\\\)。然后，我们会问自己“如果真正的差异确实为零，我们是否可能会观察到这种差异？”在统计数学术语中，我们可以将这个问题转化为检查 z 统计量离零有多远。\n",
    "\n",
    "在 \\\\(H_0\\\\) 下，z 统计量遵循标准正态分布。因此，如果差异确实为零，我们将在 95% 的时间内看到 z 统计量在平均值的 2 个标准差内。这样做的直接后果是，如果 z 高于或低于 2 个标准差，我们可以以 95% 的置信度拒绝原假设。\n",
    "\n",
    "让我们看看这在我们的课堂示例中是什么样子的。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-2.7792810791031064\n"
     ]
    }
   ],
   "source": [
    "z = diff_mu / diff_se\n",
    "print(z)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(-4,4,100)\n",
    "y = stats.norm.pdf(x, 0, 1)\n",
    "plt.plot(x, y, label=\"Standard Normal\")\n",
    "plt.vlines(z, ymin=0, ymax=.05, label=\"Z statistic\", color=\"C1\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "这看起来是一个非常极端的值。 事实上，它高于 2，这意味着如果组中没有差异，我们看到这样一个极值的可能性不到 5%。 这再次使我们得出结论，从面对面转向在线课程会导致学业成绩在统计上显着下降。\n",
    "\n",
    "关于假设检验的最后一件有趣的事情是，它不如检查治疗组和未治疗组的 95% CI 是否重叠那么保守。 换句话说，如果两组中的置信区间重叠，仍然可能出现结果具有统计显着性的情况。 例如，假设面对面组的平均分数为 80，标准误差为 4，在线组的平均分数为 71，标准误差为 2。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Control 95% CI: (67.08, 74.92)\n",
      "Test 95% CI: (72.16, 87.84)\n",
      "Diff 95% CI: (0.23461352820082482, 17.765386471799175)\n"
     ]
    }
   ],
   "source": [
    "cont_mu, cont_se =  (71, 2)\n",
    "test_mu, test_se = (80, 4)\n",
    "\n",
    "diff_mu = test_mu - cont_mu\n",
    "diff_se = np.sqrt(cont_se**2 + test_se**2)\n",
    "\n",
    "print(\"Control 95% CI:\", (cont_mu-1.96*cont_se, cont_mu+1.96*cont_se))\n",
    "print(\"Test 95% CI:\", (test_mu-1.96*test_se, test_mu+1.96*test_se))\n",
    "print(\"Diff 95% CI:\", (diff_mu-1.96*diff_se, diff_mu+1.96*diff_se))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "如果我们为这些组构建置信区间，它们就会重叠。在线组 95% CI 的上限为 74.92，面对面组的下限为 72.16。然而，一旦我们计算了组间差异的 95% 置信区间，我们可以看到它不包含零。总之，即使各个置信区间重叠，差异仍然可以在统计上不同于零。\n",
    "\n",
    "## P 值\n",
    "\n",
    "我之前说过，如果在线组和面对面组之间的差异实际上为零，我们观察到这种极端值的可能性不到 5%。但是我们能准确估计这个机会是多少吗？我们观察到这样一个极值的可能性有多大？输入 p 值！\n",
    "\n",
    "就像置信区间（以及大多数频率统计，事实上）一样，p 值的真正定义可能非常令人困惑。因此，为了不冒任何风险，我将复制维基百科的定义：“p 值是获得测试结果的概率至少与测试期间实际观察到的结果一样极端，假设原假设是正确的” .\n",
    "\n",
    "更简洁地说，p 值是看到此类数据的概率，前提是原假设为真。如果原假设为真，它衡量您看到测量结果的可能性有多大。自然地，这常常与原假设为真的概率混淆。注意这里的区别。 p 值不是 \\\\(P(H_0|data)\\\\)，而是 \\\\(P(data|H_0)\\\\)。\n",
    "\n",
    "但是不要让这种复杂性欺骗了您。实际上，它们使用起来非常简单。\n",
    "\n",
    "![p_value](./data/img/stats-review/p_value.png)\n",
    "\n",
    "要获得 p 值，我们需要计算 z 统计量之前或之后的标准正态分布下的面积。幸运的是，我们有一台计算机可以帮我们做这个计算。我们可以简单地将 z 统计量插入标准正态分布的 CDF 中。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "P-value: 0.0027239680835564706\n"
     ]
    }
   ],
   "source": [
    "print(\"P-value:\", stats.norm.cdf(z))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "这意味着如果差异为零，则只有 0.2% 的机会观察到这个极端的 z 统计量。 请注意 p 值的有趣之处，因为它避免了我们必须指定置信水平，例如 95% 或 99%。 但是，如果我们希望报告一个，根据 p 值，我们确切地知道我们的测试将通过或失败的置信度。 例如，p 值为 0.0027，我们知道我们在 0.2% 的水平上具有显着性。 因此，虽然差异的 95% CI 和 99% CI 都不包含零，但 99.9% CI 会。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "95% CI: (-8.37634655308288, -1.4480964433709733)\n",
      "99% CI: (-9.464853535264012, -0.3595894611898425)\n",
      "99.9% CI: (-10.72804065824553, 0.9035976617916743)\n"
     ]
    }
   ],
   "source": [
    "diff_mu = online.mean() - face_to_face.mean()\n",
    "diff_se = np.sqrt(face_to_face.var()/len(face_to_face) + online.var()/len(online))\n",
    "print(\"95% CI:\", (diff_mu - stats.norm.ppf(.975)*diff_se, diff_mu + stats.norm.ppf(.975)*diff_se))\n",
    "print(\"99% CI:\", (diff_mu - stats.norm.ppf(.995)*diff_se, diff_mu + stats.norm.ppf(.995)*diff_se))\n",
    "print(\"99.9% CI:\", (diff_mu - stats.norm.ppf(.9995)*diff_se, diff_mu + stats.norm.ppf(.9995)*diff_se))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 关键思想\n",
    "\n",
    "我们已经看到了解 Moivre 方程的重要性，我们用它来确定我们的估计值。 也就是说，我们发现与面对面课程相比，在线课程会导致学习成绩下降。 我们还看到这是一个具有统计意义的结果。 我们通过比较两组均值的置信区间、查看差异的置信区间、进行假设检验和查看 p 值来做到这一点。 下面，让我们将所有内容都包含在一个函数中，该函数通过A/B实验进行比较，就像我们上面所做的那样。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test 95.0% CI: 73.63526308510637 +- 3.0127770572134565\n",
      "Control 95.0% CI: 78.5474845833333 +- 1.7097768273108005\n",
      "Test-Control 95.0% CI: -4.912221498226927 +- 3.4641250548559537\n",
      "Z Statistic -2.7792810791031064\n",
      "P-Value 0.0027239680835564706\n"
     ]
    }
   ],
   "source": [
    "def AB_test(test: pd.Series, control: pd.Series, confidence=0.95, h0=0):\n",
    "    mu1, mu2 = test.mean(), control.mean()\n",
    "    se1, se2 = test.std() / np.sqrt(len(test)), control.std() / np.sqrt(len(control))\n",
    "    \n",
    "    diff = mu1 - mu2\n",
    "    se_diff = np.sqrt(test.var()/len(test) + control.var()/len(control))\n",
    "    \n",
    "    z_stats = (diff-h0)/se_diff\n",
    "    p_value = stats.norm.cdf(z_stats)\n",
    "    \n",
    "    def critial(se): return -se*stats.norm.ppf((1 - confidence)/2)\n",
    "    \n",
    "    print(f\"Test {confidence*100}% CI: {mu1} +- {critial(se1)}\")\n",
    "    print(f\"Control {confidence*100}% CI: {mu2} +- {critial(se2)}\")\n",
    "    print(f\"Test-Control {confidence*100}% CI: {diff} +- {critial(se_diff)}\")\n",
    "    print(f\"Z Statistic {z_stats}\")\n",
    "    print(f\"P-Value {p_value}\")\n",
    "        \n",
    "AB_test(online, face_to_face)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "由于我们的函数足够通用，我们可以测试其他零假设。 例如，我们是否可以尝试拒绝在线课堂和面对面课堂表现之间的差异为 -1。 根据我们得到的结果，我们可以 95% 的置信度说差异大于 -1。 但我们在99% 的置信度上却没法这么肯定："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test 95.0% CI: 73.63526308510637 +- 3.0127770572134565\n",
      "Control 95.0% CI: 78.5474845833333 +- 1.7097768273108005\n",
      "Test-Control 95.0% CI: -4.912221498226927 +- 3.4641250548559537\n",
      "Z Statistic -2.2134920404560723\n",
      "P-Value 0.013431870694630667\n"
     ]
    }
   ],
   "source": [
    "AB_test(online, face_to_face, h0=-1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 参考资料\n",
    "\n",
    "1. https://www.americanscientist.org/article/the-most-dangerous-equation"
   ]
  }
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